The Hawkes Processes is a popular type of self-exciting point process that has found application in the modeling of financial stock markets, earthquakes, and social media cascades. Their continuous time framework, however, necessitates that data collected for inference be accurate. However, for real-time monitors of data, for example in remote sensing or cybersecurity, accurate detection of events is challenging. In the first part of this talk, we develop a novel frequentist inference mechanism for binned data, i.e., continuous data that is aggregated within discrete bins upon recording. The results of this will be highlighted on real computer network data, which exhibit high levels of self-excitation. We then highlight that understanding the underlying Hawkes’ source and pattern of excitation is important for many real-world applications, such as criminal behavior.  In the second part, we develop a novel Bayesian non-parametric model for a Hawkes process whose excitation kernel is be flexibly modeled, to allow for different levels of self-excitation. The utility of this model is presented for modeling and predicting extreme terror attacks in Afghanistan.